This paper presents the acados software package, a collection of solvers for fast embedded optimization intended for fast embedded applications. Its interfaces to higher-level languages make it useful for quickly designing an optimization-based control algorithm by putting together different algorithmic components that can be readily connected and interchanged. Since the core of acados is written on top of a high-performance linear algebra library, we do not sacrifice computational performance. Thus, we aim to provide both flexibility and performance through modularity, without the need to rely on automatic code generation, which facilitates maintainability and extensibility. The main features of acados are: efficient optimal control algorithms targeting embedded devices implemented in C, linear algebra based on the high-performance BLASFEO library, user-friendly interfaces to Matlab and Python, and compatibility with the modeling language of CasADi. acados is free and open-source software released under the permissive BSD 2-Clause license.

acados: a modular open-source framework for fast embedded optimal control

OpEn: Code Generation for Embedded Nonconvex Optimization

We propose a methodology for autonomous aerial navigation and obstacle avoidance of micro aerial vehicles (MAVs) using non-linear model predictive control (NMPC) and we demonstrate its effectiveness with laboratory experiments. The proposed methodology can accommodate obstacles of arbitrary, potentially non-convex, geometry. The NMPC problem is solved using PANOC: a fast numerical optimization method which is completely matrix-free, is not sensitive to ill conditioning, involves only simple algebraic operations and is suitable for embedded NMPC. A c89 implementation of PANOC solves the NMPC problem at a rate of 20 Hz on board a lab-scale MAV. The MAV performs smooth maneuvers moving around an obstacle. For increased autonomy, we propose a simple method to compensate for the reduction of thrust over time, which comes from the depletion of the MAV's battery, by estimating the thrust constant.

/pdf/aerial-navigation-in-obstructed-environments-with-embedded-1i2moc1gpc.pdf

Aerial navigation in obstructed environments with embedded nonlinear model predictive control

This paper presents the acados software package, a collection of solvers for fast embedded optimization intended for fast embedded applications. Its interfaces to higher-level languages make it useful for quickly designing an optimization-based control algorithm by putting together different algorithmic components that can be readily connected and interchanged. Since the core of acados is written on top of a high-performance linear algebra library, we do not sacrifice computational performance. Thus, we aim to provide both flexibility and performance through modularity, without the need to rely on automatic code generation, which facilitates maintainability and extensibility. The main features of acados are: efficient optimal control algorithms targeting embedded devices implemented in C, linear algebra based on the high-performance BLASFEO Frison (ACM Transactions on Mathematical Software (TOMS) 44: 1–30, 2018) library, user-friendly interfaces to Matlab and Python, and compatibility with the modeling language of CasADi Andersson (Mathematical Programming Computation 11: 136, 2019). acados is free and open-source software released under the permissive BSD 2-Clause license.

Acados — a modular open-source framework for fast embedded optimal control

This article proposes a targeting posture control approach with dynamic obstacle avoidance of differential-drive wheeled mobile robot (WMR) systems in the presence of unknown skidding, slipping, input disturbances, model uncertainties, and torque saturation. First, a nonlinear model predictive control (NMPC) scheme is presented to generate a feasible trajectory from a starting posture to a targeting posture where dynamic obstacles in the environment and physical constraints of the robots are considered. Second, a robust virtual control law at the kinematic level is introduced for the robots to follow the trajectory. Third, taking the consideration of the unknown skidding, slipping, input disturbances, and model uncertainties in the dynamic model being lumped as a total disturbance, which is estimated by the linear extended state observer (LESO), a disturbance compensation-based saturation controller is designed to make the real velocity of the robot converge to the virtual velocity command. Finally, the effectiveness of the proposed control strategy is verified by simulation results.

Targeting Posture Control With Dynamic Obstacle Avoidance of Constrained Uncertain Wheeled Mobile Robots Including Unknown Skidding and Slipping

We employ the proximal averaged Newton-type method for optimal control (PANOC) to solve obstacle avoidance problems in real time. We introduce a novel modeling framework for obstacle avoidance which allows us to easily account for generic, possibly nonconvex, obstacles involving polytopes, ellipsoids, semialgebraic sets and generic sets described by a set of nonlinear inequalities. PANOC is particularly well-suited for embedded applications as it involves simple steps, its implementation comes with a low memory footprint and its fast convergence meets the tight runtime requirements of fast dynamical systems one encounters in modern mechatronics and robotics. The proposed obstacle avoidance scheme is tested on a lab-scale autonomous vehicle.

/pdf/embedded-nonlinear-model-predictive-control-for-obstacle-4vovcfm23y.pdf

Embedded nonlinear model predictive control for obstacle avoidance using PANOC

In this work we implement motion planning and control of a robot arm with nonlinear model predictive control using the optimization algorithm PANOC. PANOC is a first order nonlinear optimization solver, with convergence guarantees, that is matrix-free unlike the popular sequential quadratic programming and nonlinear interior-point methods. We extend this solver to deal with hard constraints using an augmented Lagrangian method. This is used to implement a multipleshooting MPC algorithm with collision avoidance capabilities on a robot arm. The computational time is benchmarked against other nonlinear optimization solvers. The algorithm is validated with simulations.

/pdf/real-time-robot-arm-motion-planning-and-control-with-3lf6tbqpob.pdf

Real-time Robot Arm Motion Planning and Control with Nonlinear Model Predictive Control using Augmented Lagrangian on a First-Order Solver

Extensive work has been done on efficiently resolving hierarchical robot task specifications that minimize the $\ell$ -2 norm of linear constraint violations, but not for $\ell$ -1 norm, in which there has recently been growing interest for sparse control. Both approaches require solving a cascade of quadratic programs (QP) or linear programs (LP). In this letter, we introduce alternate and more efficient approaches to hierarchical $\ell$ -1 norm minimization by formulating it as a single LP that can be solved by any off-the-shelf solver. The first approach is a recursive method that transforms the lexicographic LP (LLP) into a single objective problem using Lagrangian duality. The second approach, which forms the main focus of this letter, is a weighted method based on the exact penalty method, that is equivalent to the original LLP for a well chosen set of weights. We propose methods to compute and adapt these weights. The algorithms were applied on an interesting dual arm robot task. We discuss and benchmark the computational efficiency of these methods. Simplicity of the weighted method makes it a promising approach for tackling challenging prioritized robot control problems involving a control horizon or nonlinear constraints. Within this letter, we take the first step towards that goal by demonstrating the efficacy of the weighted method on a simpler instantaneous robot control problem with linear constraints.

A Weighted Method for Fast Resolution of Strictly Hierarchical Robot Task Specifications Using Exact Penalty Functions

Prioritization of tasks is a common approach to resolve conflicts in instantaneous control of redundant robots. However, the idea of prioritization has not yet been satisfactorily extended to model predictive control (MPC) to allow for real-time robot control. The standard sequential approach for prioritization is unsuitable because of the computational burden involved in solving a nonlinear problem (NLP) at every priority level. We introduce an alternate promising approach of using weighted exact penalties for the MPC stage costs, where a correctly tuned set of weights can introduce strict prioritization. We prove the existence of a set of equivalent weights that provides the same solution as the sequential approach for a local convex approximation of the original NLP and use this insight to design an algorithm to adaptively tune the weights. The weighted method is validated on a dual arm robot task in simulations and also implemented on a physical robot. We report computational times that are fast enough for prioritized MPC of robot manipulators for the first time, to the best of our knowledge.

/pdf/a-simple-formulation-for-fast-prioritized-optimal-control-of-r4ixmw0o.pdf

A Simple Formulation for Fast Prioritized Optimal Control of Robots using Weighted Exact Penalty Functions

The programming of complex tasks with robot manipulators faces the challenges of complying to constraints and needing to account for several, sometimes conflicting performance objectives. Optimal control problems (OCP) are able to explicitly account for these challenges by solving constrained optimization problems to find optimal trajectories that realize such tasks. The wide adoption of OCPs, however, is restricted by the high engineering cost and the high computational complexity associated to its implementation. To that end, in this paper we present a web application and graphical user interface (GUI) that acts as a front-end of Tasho, a toolbox for constrained-based task specification of robot motion tasks. This web application aims to lower the engineering complexity of setting, simulating and deploying a robot task by realizing a direct workflow from task definition on the GUI to deployment on a real robot using ROS. By interfacing state-of-the-art solvers and libraries through Tasho, the web application delivers computationally efficient solutions to the OCPs associated to the task. 

Ajay Suresha Sathya

Papers

Embedded nonlinear model predictive control for obstacle avoidance using PANOC

Real-time Robot Arm Motion Planning and Control with Nonlinear Model Predictive Control using Augmented Lagrangian on a First-Order Solver

A Weighted Method for Fast Resolution of Strictly Hierarchical Robot Task Specifications Using Exact Penalty Functions

A Simple Formulation for Fast Prioritized Optimal Control of Robots using Weighted Exact Penalty Functions

A Web-Based Graphical User Interface for Programming Optimal Control Based Robot Motion Tasks